Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 1520 and 1524 the smallest integer that is 579120 that is divisible by both numbers.
Least Common Multiple (LCM) of 1520 and 1524 is 579120.
LCM(1520,1524) = 579120
Least common multiple or lowest common denominator (LCD) can be calculated in three ways;
Least common multiple can be found by multiplying the highest exponent prime factors of 1520 and 1524. First we will calculate the prime factors of 1520 and 1524.
Prime Factorization of 1520
2 | 1520 |
2 | 760 |
2 | 380 |
2 | 190 |
5 | 95 |
19 | 19 |
1 |
Prime factors of 1520 are 2, 5,19. Prime factorization of 1520 in exponential form is:
1520 = 24×51×191
Prime Factorization of 1524
2 | 1524 |
2 | 762 |
3 | 381 |
127 | 127 |
1 |
Prime factors of 1524 are 2, 3,127. Prime factorization of 1524 in exponential form is:
1524 = 22×31×1271
Now multiplying the highest exponent prime factors to calculate the LCM of 1520 and 1524.
LCM(1520,1524) = 24×31×51×191×1271
LCM(1520,1524) = 579120
Factors of 1520
List of positive integer factors of 1520 that divides 1520 without a remainder.
1, 2, 4, 5, 8, 10, 16, 19, 20, 38, 40, 76, 80, 95, 152, 190, 304, 380, 760, 1520
Factors of 1524
List of positive integer factors of 1524 that divides 1524 without a remainder.
1, 2, 3, 4, 6, 12, 127, 254, 381, 508, 762, 1524
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1520 and 1524, than apply into the LCM equation.
GCF(1520,1524) = 4
LCM(1520,1524) = ( 1520 × 1524) / 4
LCM(1520,1524) = 2316480 / 4
LCM(1520,1524) = 579120
(i) The LCM of 1524 and 1520 is associative
LCM of 1520 and 1524 = LCM of 1524 and 1520
1. What is the LCM of 1520 and 1524?
Answer: LCM of 1520 and 1524 is 579120.
2. What are the Factors of 1520?
Answer: Factors of 1520 are 1, 2, 4, 5, 8, 10, 16, 19, 20, 38, 40, 76, 80, 95, 152, 190, 304, 380, 760, 1520. There are 20 integers that are factors of 1520. The greatest factor of 1520 is 1520.
3. What are the Factors of 1524?
Answer: Factors of 1524 are 1, 2, 3, 4, 6, 12, 127, 254, 381, 508, 762, 1524. There are 12 integers that are factors of 1524. The greatest factor of 1524 is 1524.
4. How to Find the LCM of 1520 and 1524?
Answer:
Least Common Multiple of 1520 and 1524 = 579120
Step 1: Find the prime factorization of 1520
1520 = 2 x 2 x 2 x 2 x 5 x 19
Step 2: Find the prime factorization of 1524
1524 = 2 x 2 x 3 x 127
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 579120 = 2 x 2 x 2 x 2 x 3 x 5 x 19 x 127
Step 4: Therefore, the least common multiple of 1520 and 1524 is 579120.